Perhaps this should be in the Product Claims subforum, but I can't imagine how long it'd take to build up even a few dozen mAh of charge with 40 mW routers. Perhaps as an emergency, always available source, but as something used on a regular basis? I don't know if I buy it.

Sounds like total nonsense.
Bear in mind
1. the efficiency of the Router transmitter, in terms of total power supplied vs actual transmitted RF power and
2. The loss of power over the RF link (assuming you're not in an ellipsoidal reflecting box with Tx and Rx at the foci)

I agree that it sound fishy, But there are a number of companies working on this and some of them have a pretty good reputation when it comes to innovations I might be wrong but I think I've read somewhere that Nokia are working on something similar and have already demonstrated a prototype It wouldn't give you enough energy to actually charge the battery if it it was empty, but the claim is that this technique might improve battery life somewhat.

Despite their possibly good reputations you can't argue with the figures, can you? You're talking tens or hundreds of microWatts, tops, when you're close to the transmitter. Let's face it - they use a receiver with an amplifier, to produce enough power to detect and decode the actual WiFi signal. Why would they bother, if there was enough received power to operate a "crystal set'?
A much better potential source of energy would be movement (like kinetic watches) or thermal.

But there are quite a few devices that only require a say 100 uW in standby-mode, and for those it might be a useful technique for extending battery life; at least when combined with a battery.

Also, the "harvester" would presumably be a separate circuit, it would obviously not make sense to operate it while using an amplifier at the same time so the rest of the RF circuitry would have to be in standby mode when using the harvester (and maybe only respond to a very simple and strong "wakeup" signal).

This feels wrong to me. The maximum permitted radiated power from a WiFi device is, according to Wikkers, 100mW and this would be radiated omnidirectionally, more or less. It would be very lucky to get as little as 30dB of loss between transmitter and receiver - without my silly scenario or a dedicated, directional antenna at each end. This would make even a modest 100uW much too much to hope for.

When you think that 100uW is the sort of power that a tiny battery would give you for months, in any case, I really question it as being worthwhile, at all. It is insignificant compared with the load which the 'main' equipment would be needing - even for a few minutes at a time (we're looking at very esoteric applications here, at best and not a domestic scenario). A device which would need to run for a long time without attention would be, necessarily, a long way from a base station and be receiving the very minimum of signal strength.
There are occasional threads on fora about 'wireless power transmission' and this seems to be another of the same. We could just as well discuss the possibility of having a Radio receiver which we could use once in a blue moon which is operated by off-air power. Anyone who has made a crystal set will know that you need a pretty huge aerial installation to get energy out of the Aether. That tends to be true whatever frequency you are working at.